A court has been told the jury that convicted Keli Lane of murdering her newborn baby should have been allowed to consider a less serious charge.

The former water polo champion smiled and waved at family members supporting her case in front of a three-judge panel at the NSW Court of Criminal Appeal.

Lane, 38, was jailed for at least 13 years and five months in 2011 for murdering her newborn daughter Tegan, whose body has never been found.

The girl was last seen leaving Auburn Hospital two days after being born in 1996.

Lane has always maintained she gave Tegan to the child's biological father, a man called Andrew Norris or Morris, with whom she had a secret affair.

Her barrister, Winston Terracini SC, today told the Court of Criminal Appeal that evidence in the case was circumstantial and the jurors who convicted Lane of murder were constrained from considering alternative charges including manslaughter.

Mr Terracini said Tegan may have been unlawfully killed but it might have been without intent.

He said the Crown could not rule out that the baby was dropped or died after being put in a bag.

Two of the judges suggested to Mr Terracini that he did not have any new evidence to back his claim that the jury should have been given the option of manslaughter to consider.

Mr Terracini replied "the Crown can't do any better", and said the prosecution case of murder was just speculation.

"She certainly did not exhibit any animosity or lack of bonding with her child when she left the hospital," he said.

Mr Terracini drew comparisons in Lane's case to that of Gordon Wood, who was acquitted last year of murdering his model girlfriend Caroline Byrne.

'A situation of desperation'

When Lane was found guilty after a week of deliberations, there were dramatic scenes in court when she fainted and an ambulance was called.

In sentencing, Justice Anthony Whealy said she murdered Tegan "in a situation of desperation" and felt that she could not turn to people close to her for help.

The judge said the case was "a tragedy involving mother and daughter" and that the life of a defenceless baby had been taken.

The trial jury heard Lane had five secret pregnancies, including two terminations and two children she adopted out.

In February she lost an application for bail ahead of the appeal hearing.